360 Mr. A. Stephenson on 
proportional to the fourth power o£ the swing. Hence, i£ E 
is the energy of the motion at time t, 
dt 1 
where q a constant. This gives 
F- JL 
G + qt' 
where C = 1/E ; therefore 
clE_ q 
dt ~~ (C + qty 
Now I, the intensity of the phosphorescence, is equal to 
the rate of energy emission ; thus 
i-i=, r i. ( c+,,o, 
i. e., the reciprocal of the square root of the emission intensity 
has a uniform time gradient. 
The initial intensity is proportional to the square of the 
total store, and therefore increases proportionally with the 
incident intensity until the latter becomes so large that our 
approximation (vi.) does not apply. 
6. It may be well now to summarise the properties of the 
system as regards phosphorescence in the probable order of 
their appearance to an experimental observer : — 
1. The emission frequency is independent of the exciting- 
disturbance. 
2. The system stores energy under incident disturbance 
of any frequency within a certain range which 
includes the emission frequency ; the greater the 
intensity of disturbance the greater the range and the 
greater the excess of its cenlral value above the emission 
frequency. 
3. For different frequencies within the range the initial 
rate of energy storage is maximum near the centre, 
and decreases gradually towards each end. If the 
frequency of the storing coordinate is less than half the 
frequency of the other, the system ultimately reaches 
a steady state only for that part of the range which 
lies above the emission frequency. In the steady state 
the energy stored is proportional to the square root of 
the incident intensity, and it also varies with the 
applied frequency, gradually decreasing to zero as 
the latter is taken greater within the range. 
